Definability equals recognizability for graphs of bounded treewidth

We prove a conjecture of Courcelle, which states that a graph property is definable in MSO with modular counting predicates on graphs of constant treewidth if, and only if it is recognizable in the following sense: constant-width tree decompositions of graphs satisfying the property can be recognized by tree automata. While the forward implication is a classic fact known as Courcelle's theorem, the converse direction remained openComment: 21 pages, an extended abstract will appear in the proceedings of LICS 201

Anatomical landmark based registration of contrast enhanced T1-weighted MR images

In many problems involving multiple image analysis, an im- age registration step is required. One such problem appears in brain tumor imaging, where baseline and follow-up image volumes from a tu- mor patient are often to-be compared. Nature of the registration for a change detection problem in brain tumor growth analysis is usually rigid or affine. Contrast enhanced T1-weighted MR images are widely used in clinical practice for monitoring brain tumors. Over this modality, con- tours of the active tumor cells and whole tumor borders and margins are visually enhanced. In this study, a new technique to register serial contrast enhanced T1 weighted MR images is presented. The proposed fully-automated method is based on five anatomical landmarks: eye balls, nose, confluence of sagittal sinus, and apex of superior sagittal sinus. Af- ter extraction of anatomical landmarks from fixed and moving volumes, an affine transformation is estimated by minimizing the sum of squared distances between the landmark coordinates. Final result is refined with a surface registration, which is based on head masks confined to the sur- face of the scalp, as well as to a plane constructed from three of the extracted features. The overall registration is not intensity based, and it depends only on the invariant structures. Validation studies using both synthetically transformed MRI data, and real MRI scans, which included several markers over the head of the patient were performed. In addition, comparison studies against manual landmarks marked by a radiologist, as well as against the results obtained from a typical mutual information based method were carried out to demonstrate the effectiveness of the proposed method